The game will be Grayson's first Carling Cup tie in charge of Leeds
Leeds United manager Simon Grayson has said he will be taking the Carling Cup seriously after being drawn away to Darlington in the first round.
The competition starts in early August, when Leeds will have only played one league game.
But Grayson told the club's website they will be treating the competition as a priority: "The Carling Cup is an important part of our campaign."
The tie at the Darlington Arena is set for the week commencing 10 August
Grayson added: "The first round comes up very quickly, we will have played only one league game at that stage, and it can be a good early platform for us.
"Darlington have a new manager in Colin Todd, who I know well, and they will be looking for a positive start under him."
Grayson won the League Cup as a player with Leicester City in 1997 when he was a member of the side that beat Middlesbrough 1-0 after extra time in a replay at Hillsborough.
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